Exercise machines for simulating walking or running are known and used for directing the movement of a user's legs and feet in a variety of repetitive paths of travel. Machines commonly referred to as elliptical path machines have been designed to pivot the foot pedals on which the user's feet reside causing the pedals and the user's feet to travel in an elliptical path. The path of travel of the foot pedals in such prior machines is different from front to back and the angular degree of pivoting of the foot pedals changes as the foot pedal travels from back to front and front to back by typically more than about 3 degrees and more typically more than 10-30 degrees.